"Prior attribution" is when a user arrives on the site via organic traffic (search engines, direct access, referrer sites...) while having come to the site from a marketing campaign previously; the campaign information is stored in a cookie.
As such, a Visit (prior attribution) is a visit made after a visit coming from a campaign, that can be retroactively attributed to that previous campaign.
This is particularly useful to identify users having come to the site for a specific promotional offer, but only having converted in a later visit which didn't originate from the same source.